However, those computational and statistical gains are paid at the price of losing metrization of weak* topology.
In fact, for any \((,)\in ()\) , it does not satisfy \((,)=0\)  and even worse, one has in general \(\notin \arg \min (\cdot ,)\) .
Consequently, training via gradient descent does not produce a model such that \(_\simeq \) .
More precisely, it is shown in [1]} that if \(\epsilon \rightarrow +\infty \) , then \(^\star =\arg \min _(,)\)  degenerates to a Dirac mass \(_{x^\star }\) , where
\(x^\star = \arg \min _{z\in }\int z, y)(y).\) 
